If you look back at some old threads about where to stay in Paris, you will see that there is on ongoing argument about this. Based on my personal experience and all of the opinions I have read here I would advise this:
Stay close to a metro stop or bus stop so that you can get around easily. Stay relatively close to the Seine for your first trip, again to make getting to sites less time consuming and easier.
With kids, I would recommend using Google street view and taking a little "walk" around to see if it will be a place that the kids can run to the boulangerie or market on their own or if you might need to accompany them.
Otherwise, stay anywhere that your budget allows.
I was in Paris for 2 weeks. The first week I stayed in the much maligned 7th (near the Eiffel tower). I loved the neighborhood! It was great walking down Rue Cler, there were a lot of small cafe's , bakeries, high end restaurants, you name it.
The second week I stayed in the 1st near the Louvre and Rue Rivoli. A lot of people feel this area is to "industrial". I didn't really hang out in the direct vicinity, but I was a 5 minute walk to the Tuileries garden. I spent a lot of time in the garden with a paperback book. I could get anywhere from the Tuileries metro stop pretty easily. I loved both neighborhoods.
I am going back in May and this time I chose St. Germain de Pres for lodging. My plan is to stay in every neighborhood, eventually.
Have a great trip!